<h2>Problem 9</h2>
<div style="color:#666;font-size:80%;">25 January 2002</div><br />
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<p>A Pythagorean triplet is a set of three natural numbers, <var>a</var> <img src='images/symbol_lt.gif' width='10' height='10' alt='&lt;' border='0' style='vertical-align:middle;' /> <var>b</var> <img src='images/symbol_lt.gif' width='10' height='10' alt='&lt;' border='0' style='vertical-align:middle;' /> <var>c</var>, for which,</p>
<div style="text-align:center;"> <var>a</var><img src="" style="display:none;" alt="^(" /><sup>2</sup><img src="" style="display:none;" alt=")" /> + <var>b</var><img src="" style="display:none;" alt="^(" /><sup>2</sup><img src="" style="display:none;" alt=")" /> = <var>c</var><img src="" style="display:none;" alt="^(" /><sup>2</sup><img src="" style="display:none;" alt=")" /></div>
<p>For example, 3<img src="" style="display:none;" alt="^(" /><sup>2</sup><img src="" style="display:none;" alt=")" /> + 4<img src="" style="display:none;" alt="^(" /><sup>2</sup><img src="" style="display:none;" alt=")" /> = 9 + 16 = 25 = 5<img src="" style="display:none;" alt="^(" /><sup>2</sup><img src="" style="display:none;" alt=")" />.</p>
<p>There exists exactly one Pythagorean triplet for which <var>a</var> + <var>b</var> + <var>c</var> = 1000.<br />Find the product <var>abc</var>.</p>

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